Answer:
[tex]\omega_2=0.891\ rev/s[/tex]
Explanation:
Given that
Radius , r= 3.03 m
Mass of disk , M= 145 kg
Initial angular velocity
ω=0.681 rev/s
Mass of person , m= 65.4 kg
Velocity of person , V= 3.41 m/s
Initial mass moment of inertia
[tex]I_1= \dfrac{M\times R^2}{2}[/tex]
[tex]I_1= \dfrac{145\times 3.03^2}{2}=665.61\ kg.m^2[/tex]
Final mass moment of inertia
[tex]I_2= \dfrac{M\times R^2}{2}+m\times R^2[/tex]
[tex]I_2= \dfrac{145\times 3.03^2}{2}+65.4\times 3.03^2=1266.04\ kg.m^2[/tex]
[tex]Final\ angular\ velocity =\omega_2[/tex]
By using angular momentum equation
[tex]I_1\times \omega+m\times V\times R=I_2\times \omega_2[/tex]
[tex]665.61\times 0.681+65.4\times 3.41\times 3.03=1266.04\times \omega_2[/tex]
[tex]1129.01= 1266.04\times \omega_2[/tex]
[tex]\omega_2=\dfrac{1129.01}{1266.04}[/tex]
[tex]\omega_2=0.891\ rev/s[/tex]
Thus the angular velocity will be 0.891 rev/s
